Merge (fuse) two meshes together
Create Hole. Mesh LoopTools Addon. Extrude and Shape.




Simplified Shapes.  A Box representing your lantern.  
Suggestion change your mesh model construction technique as indicated below.
Faces Removed. Counting edges to match a destination shape.  Appropriate vertex density.
Square hole shaped to circular with LoopTools Circle.
Extruded.  Shaped with Proportional Edit. We see a continous well shaped extrusion rather than two meshes islands intersecting.
Now you can align the base with the two (side supports) to create a continuous surface.  You can use Bridge Edge Loops for that.  This is not shown but is certainly shown here at BSE on other questions.
Weld Pattern Options


Torus modified with Proportional Edit / Displacement Textures as an optional separate Mesh. 
Higher (localized) vertex density for weld patterns 
Texture paint
Not Recommended Particle System unless Spheres